Heat a non-stick skillet over high heat. Using 1 tablespoon of vegetable oil, brown the hash browns. Season the cooking hash browns with the thyme, salt, and pepper. Once brown set aside in a mixing bowl. With the remaining oil, brown and carmelize the onions. Once the onions are done, add the sweet potatoes. Cook, stirring occasionally until the sweet potatoes are tender. Add the turkey kielbasa and cook for 3-4 minutes. Add the sweet potato mixture to the previously cooked hash browns. Mix together with the Dijon mustard. Add the hash mixture back to the pan and cook for an additional 3-4 minutes at medium heat. While the hash is cooking, fry the eggs in a non-stick skillet. Serve the hash with the fried egg on top.